Question

Abc inc. is planning the production schedule for the next 8 weeks. the forecasted demand for the next 8 weeks is 700, 800, 900, 500, 1100, 1000, 800, and 900 respectively. abc can produce 800 units per week in regular time and 200 more in overtime. the regular time production cost is $10.00 per unit which takes into account $4.00 for materials, $1.00 for utilities, and $5.00 for manpower. the manpower cost for overtime is twice the regular rate. holding a unit in inventory costs $1 per unit per week. there is also a cost for been late, at $2.00 per unit per week. the maximum lateness allowed is 2 weeks. it is the company's policy not to have any item in inventory for more than 3 weeks. how much should abc produce each week?

Answer 1

There are two options for the company to produce:

1. To produce 800 units per week,
2. To produce as required number of units.

First option:

Produce 800 units per week:

Particulars	Week 1	Week 2	Week 3	Week 4	Week 5	Week 6	Week 7	Week 8
Demand	700	800	900	500	1100	1000	800	900
Production	800	800	800	800	800	800	800	800
Excess production/Holding	100	-	- (since earlier excess utilized after 2 weeks)	300	- (since utilised excess 300 units after 1 week)	200	-	- (since utilised excess 100 units after 2 weeks)
Production cost per unit	$10	$10	$10	$10	$10	$10	$10	$10
Total production cost= (d*b)	$8,000	$8,000	$8,000	$8,000	$8,000	$8,000	$8,000	$8,000
f.)Overtime cost	-	-	-	-	-	-	-	-
g.)Inventory Holding cost	1	1	1	1	1	1	1	1
h.)Total Holding cost (g*c)	(100*2)= $200	-	-	(300*1)=$300	-	-	-	(200*2)=$400
i.)Total All cost = (e+h)	8200	8000	8000	8300	8000	8000	8000	8400

Therefore, total cost of Regular production= $(8200+8000+8000+8300+8000+8000+8000+8400)= $64,900

Second option:

Produce as required units per week:

Particulars	Week 1	Week 2	Week 3	Week 4	Week 5	Week 6	Week 7	Week 8
Demand	700	800	900	500	1100	1000	800	900
Production	700	800	900	500	1100	1000	800	900
Overtime production	-	-	100	-	300	200	-	100
Production cost per unit	$10	$10	$10	$10	$10	$10	$10	$10
Total production cost= (d*b)	$7,000	$8,000	$9,000	$5,000	$11,000	$10,000	$8,000	$9,000
f.) Extra Overtime production cost	15	15	15	15	15	15	15	15
g.)Total overtime production cost= f*c	-	-	1500	-	4500	3000	-	1500
h.)Total All cost = (e+g)	7000	8000	10,500	5000	15500	13000	8000	10,500

Therefore, total cost of Regular production= $(7000+8000+10500+5000+15500+13000+8000+10500)= $77500

First option to produce 800 units per week is the best.